All about flooble | fun stuff | Get a free chatterbox | Free JavaScript | Avatars    
perplexus dot info

Home > Just Math
Sawtooth Sum Settlement (Posted on 2023-09-17) Difficulty: 3 of 5
Does this relationship hold true for every positive real number n?

{√(1)}+{√(2)}+{√(3)}+...+{√(n2)} ≤ ((n2-1)/12)

• If not, provide an example.
• If so, prove it.

Note: ⌊x⌋ is floor of x, which is the greatest integer less than or equal to x, and: {x} = x-⌊x⌋.

No Solution Yet Submitted by K Sengupta    
No Rating

Comments: ( Back to comment list | You must be logged in to post comments.)
Some Thoughts evidence Comment 1 of 1

A graph shows the bound itself (in blue) is pretty weak.  I added what appears to be a stronger bound (in purple.)

The function itself shows some interesting structure if you zoom out.

  Posted by Jer on 2023-09-17 11:34:43
Please log in:
Remember me:
Sign up! | Forgot password

Search body:
Forums (0)
Newest Problems
Random Problem
FAQ | About This Site
Site Statistics
New Comments (4)
Unsolved Problems
Top Rated Problems
This month's top
Most Commented On

Copyright © 2002 - 2023 by Animus Pactum Consulting. All rights reserved. Privacy Information